From the office of Apple Inc.
Research and Design
Dr. Avona Etalopartxe
Notice, this missive is not intended for unauthorized viewing. Such use of this message constitutes a
violation of the intellectual property rights of Apple Inc. and will be met with legal repercussions.
Dear Student,
We got your information from your statistics teacher, and he said you would happy to help us analyze
our data. I’m sorry we can’t visit you personally, but budget cuts mean we can’t fly to Wyoming from
California anymore. We’re hoping this message has all the information you need in it, and if not feel
free to email us. We are willing to provide an ITunes gift card for up to $100 K.
Motivation
My office is in the research and design section of Apple and we are developing a new product called the
iPhone XP. It’s going to be bigger than any iPhone yet, and it’s going to be much stronger. The reason it
will be stronger is that we are using webs from the Brazilian Tinrub spider.
Methods
Our goal right now is to maximize the amount of webbing we can get from the spiders in our labs. The
arachnologists suggest that the Tinrub spider’s ability to produce webs is based on the temperature (in
Fahrenheit). To find out we grabbed a couple dozen spiders and put them in our lab at a bunch of
different temperatures. The warming plates under each spider’s tank kept that tank at a specific
temperature.
We also randomly selected what to feed the spider for the week before we began the measurements.
The different diets offered were:
1) fire ants - we think they might help with the acidic compounds needed to create webs
2) butterflies - since they are larger they might have a higher nutritional value
3) worms – not a spider’s normal diet, but they are super cheap
4) vitamin supplements – the arachnologists tell us these vitamin capsules provide all the nutrition
a spider should need.
On a specific day cleaned each cage and 24 hours later we took all the new webbing to weigh it. The
amount of webbing in a 24 hour period is what we are interested in being able to predict or to
maximize. We assume the webbing has consistent mass per ounce.
We expected this to be the end of our experiment, but we learned that a lab assistant left rock music
playing all that night (accidentally). Thanks to surround sound all the spiders would have heard the
blaring noise equally. We decided to collect the new webs the next day (after 24 hours) and weigh them
because we were curious about the effect of the noise.
Dataset
The data set has five variables:
1) Spider – the number for that spider. Also the number for the tank the spider was put into.
2) Threadweight – the weight of the threads (measured before the night of rock) in grams
3) Temperature – the temperature in Fahrenheit
4) Diet – the insect or vitamin fed to the spider
5) Threadrock – the weight of the threads (measured after the night rock music was played)
Goals
How can we maximize the amount of webbing from these spiders?
Can we predict how much webbing a spider will create in 24 hours?
Does the temperature affect the thread weight?
Does the type of diet affect the effect of temperature on the thread weight?
Does loud noise (rock) affect the thread weight?
Does it matter if we use the vitamin supplement?
To be very precise we need the following:
1) Is the average thread weight without music different than the average with rock music?
(Regardless of temperature or diet)
2) Do vitamins cause differing average thread weight than the other diets?
(When the other diets are combined together – in a quiet environment)
3) What is the effect of temperature on the thread weight?
(Regardless of diet – in a quiet environment)
4) What is the effect of temperature on thread weight accounting for the different diets?
(In a quiet environment)
5) What equation can we use to predict the thread weight?
6) If the spiders were in the manufacturing plant (where it is quiet) where the temperature is
consistently at 78° F, and we fed them worms (because it’s cheaper) how much would we
expect each spider to produce (in weight)?
Deliverables
In order to receive your $100K ITunes gift card please provide a report that has the following aspects:
a) Introduction – A title, then a short explanation of what data you are analyzing and why it
matters. A paragraph, or a few paragraphs.
b) Graphs – any pictures that explain what the data looks like. For each picture have a sentence
explaining what you see in the picture. Any graph that does not have a sentence is
inappropriate. Be sure the graph has a title, variables are labelled, and the axis is labelled.
c) A paragraph (at least) for each of the six questions listed above. I have to report your findings to
the CEO, and I flunked Math 1400, so don’t include anything in there I can’t defend or
understand. I never had statistics and don’t ever want to.
d) Conclusion – One paragraph what you believe would be the value of your report.
e) Appendix for the statistician – We have a PhD level statistician that will review your work for
accuracy. We can’t afford to have him do the analysis, only to check your work. He has
requested specific things in your report as detailed below. Please include that stuff in an
appendix which comes after your report.
Statistical Appendix
Since I don’t understand statistics, I will just copy and paste what the statistician emailed me:
Dear Avona,
When you have the analysis done on your report please ask the student to include an appendix with the
following:
1) Any explanation for changing the data set (so that I can duplicate their work if I need to)
a. Any data points changed or deleted (and justify why you choose to change vs delete)
b. Any reorganizing of the data for the purpose of the analysis (Explain what and why)
2) Six sections, one section for each of the six questions you told me about. Make sure each
section has:
a. A sentence explaining which statistical test was used, and why. The choices are:
i. Z test for a mean
v. Matched Pairs t-test
ii. T test for a mean
vi. Simple Linear Regression
iii. Two sample means t-test
vii. Regression with a categorical effect
iv. Two sample pooled t-test
viii. Regression with a categorical interaction
b. A justification that the assumptions for the test in part a. are valid
c. The null and alternative for the test (in symbols or in English or both)
d. The alpha value used
e. The p-value of the test
f. A one sentence explanation your conclusion for the test.
g. Computer output from the program used for the analysis
Thank you for your help!
Avona Etalopartxe
Research and Development
Apple Incorporated
Logistics
This mid-term project is worth 20% of your grade in this class. The scenario of a client from Apple is fun,
but remember that your grade on this project does affect your grade in the class. I am grading the use
of proper English, correct statistical language, completion of the expectations, and adherence to the
instructions. The score is in terms of the $100 K offered, which is a fun way of saying it will be worth 100
points. Each person will receive a unique data set.
You are not allowed to discuss your analysis or results with anyone else in the class. You may discuss it
with me or Jared or Kim, but I will not grade your work beforehand. I want this to be a measure of your
ability to handle an advanced statistical analysis on your own. Any discussion of your results or the
analysis you ran with other students in the class constitutes cheating. You are allowed to have another
person (not in the class) read your paper for grammatical or literary errors.